Four positive integers $A$, $B$, $C$ and $D$ have a sum of 64. If $A+3 = B-3 = C \times 3 = D \div 3$, what is the value of the product $A \times B \times C \times D$?
Explanation: We have that $A + B + C + D = 64$.  Substituting everything in terms of $C$, we find that $(3C - 3) + (3C + 3) + C + (9C) = 64$, which means that $C = 4$.  Thus $A = 9$, $B = 15$, and $D = 36$.  Therefore our desired answer is $9\cdot 15\cdot 4\cdot 36 = \boxed{19440}$.